Pinning control of cluster synchronization in regular networks

The authors study the control of cluster synchronization in regular networks by the scheme of pinning couplings. The authors show numerically and mathematically that by changing the number and locations of the pinning nodes, a regular network can be controlled to different cluster synchronization states. This study shows the flexibility of regular networks in generating cluster synchronization, and highlights, from a different perspective, the importance of network symmetry on cluster synchronization.

[1]  S. Strogatz,et al.  Chimera states for coupled oscillators. , 2004, Physical review letters.

[2]  Yafeng Wang,et al.  Cluster synchronization in networked nonidentical chaotic oscillators. , 2019, Chaos.

[3]  Ying-Cheng Lai,et al.  Generic behavior of master-stability functions in coupled nonlinear dynamical systems. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Ying Wang,et al.  Controlling synchronous patterns in complex networks. , 2015, Physical review. E.

[5]  L. Pecora.  Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems , 1998 .

[6]  G. Hu,et al.  Instability and controllability of linearly coupled oscillators: Eigenvalue analysis , 1998 .

[7]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[8]  Francesco Sorrentino,et al.  Complete characterization of the stability of cluster synchronization in complex dynamical networks , 2015, Science Advances.

[9]  Liang Wang,et al.  Cluster synchronization in complex network of coupled chaotic circuits: An experimental study , 2018, 1804.00881.

[10]  Lei Yang,et al.  On the pinning strategy of complex networks , 2010, ArXiv.

[11]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[12]  Adilson E Motter,et al.  Network-complement transitions, symmetries, and cluster synchronization. , 2016, Chaos.

[13]  Martin Hasler,et al.  Simple example of partial synchronization of chaotic systems , 1998 .

[14]  Martin Golubitsky,et al.  Recent advances in symmetric and network dynamics. , 2015, Chaos.

[15]  Carroll,et al.  Short wavelength bifurcations and size instabilities in coupled oscillator systems. , 1995, Physical review letters.

[16]  Hansel,et al.  Clustering and slow switching in globally coupled phase oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  H. Cerdeira,et al.  Partial synchronization and spontaneous spatial ordering in coupled chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Francesco Sorrentino,et al.  Cluster synchronization and isolated desynchronization in complex networks with symmetries , 2013, Nature Communications.

[19]  Jing Zhang,et al.  Synchronization of coupled metronomes on two layers , 2017 .

[20]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[21]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[22]  Liang Huang,et al.  Topological control of synchronous patterns in systems of networked chaotic oscillators , 2013 .

[23]  Tianping Chen,et al.  Cluster synchronization in networks of coupled nonidentical dynamical systems. , 2009, Chaos.

[24]  J. Slotine,et al.  Symmetries, stability, and control in nonlinear systems and networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  J. Kurths,et al.  Hierarchical synchronization in complex networks with heterogeneous degrees. , 2006, Chaos.

[26]  Xingang Wang,et al.  Inducing isolated-desynchronization states in complex network of coupled chaotic oscillators. , 2016, Physical review. E.

[27]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[28]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Zhigang Zheng,et al.  Partial synchronization on complex networks , 2006 .

[30]  Liang Huang,et al.  Synchronization transition in networked chaotic oscillators: the viewpoint from partial synchronization. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Belykh,et al.  One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Adilson E Motter,et al.  Topological Control of Synchronization Patterns: Trading Symmetry for Stability. , 2019, Physical review letters.

[33]  Mauricio Barahona,et al.  Graph partitions and cluster synchronization in networks of oscillators , 2016, Chaos.

[34]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[35]  Ying Zhang,et al.  Experimental investigation of partial synchronization in coupled chaotic oscillators. , 2003, Chaos.

[36]  A. Pikovsky,et al.  Resolving clusters in chaotic ensembles of globally coupled identical oscillators. , 2001, Physical review letters.

[37]  Louis Pecora,et al.  Symmetry- and input-cluster synchronization in networks. , 2018, Physical review. E.

[38]  Seth Fraden,et al.  Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters. , 2019, Physical review letters.

[39]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.